In this paper, we defined the associated graph constructed to a cellular folding defined on regular CW-complexes. These graphs declare the effect of a cellular folding on the complex. Besides we studied the properties of this graph and we proved that it is connected and vertex transitive if the cellular folding is neat. Finally, by using chain maps and homology groups we obtained the necessary and sufficient conditions for a cellular map to be cellular folding and neat cellular folding respectively.
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